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4.5 Graphs of Sine and Cosine Functions Students will sketch the graphs of basic sine and cosine functions. Students will use amplitude and period to help.

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Presentation on theme: "4.5 Graphs of Sine and Cosine Functions Students will sketch the graphs of basic sine and cosine functions. Students will use amplitude and period to help."— Presentation transcript:

1 4.5 Graphs of Sine and Cosine Functions Students will sketch the graphs of basic sine and cosine functions. Students will use amplitude and period to help sketch the graphs of sine and cosine functions. Students will sketch translations of graphs of sine and cosine functions. Students will use sine and cosine functions to model real-life data.

2 Evaluate the Sine Curve using the unit circle

3 x y (0, 1) 90° (–1, 0) 180° (0, –1) 270° (1, 0) 0° 60° 45° 30° 330° 315° 300° 120° 135° 150° 210° 225° 240°

4 The Sine Curve

5 Evaluate the Cosine Curve using the unit circle

6 x y (0, 1) 90° (–1, 0) 180° (0, –1) 270° (1, 0) 0° 60° 45° 30° 330° 315° 300° 120° 135° 150° 210° 225° 240°

7 The Cosine Curve

8 Section 4.5, Figure 4.44, Key Points in the Sine and Cosine Curves, pg. 288

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10 Graph y = sin x and y = 2 sin x on your graphing calculator. Notice that the height of the hump has changed. In the equation y = a sin x is known as the amplitude of the function.

11 Graph y = cos x and y = cos 2x on your graphing calculator. Notice that the length of the curve has changed. In the equation y = cos bx, b affects the period of the function. Using sin and cos

12 Find the period and amplitude p. 294 #1

13 Find the period and amplitude p. 294 #11

14 Describe the relationship between the graphs of f and g. Consider amplitudes, periods, and shifts. p. 294 #15

15 Describe the relationship between the graphs of f and g. Consider amplitudes, periods, and shifts. p. 294 #21

16 Sketch the graphs of f and g in the same coordinate plane. (Include two full periods.) p. 294 #27

17 Reference Graphs y = sin x y = cos x

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